Diffusive Instabilities and Pattern Formation in the Belousov-Zhabotinsky System
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Complex dynamics of certain types of chemical systems like the Belousov-Zhabotinsky reaction has been attracting the attention of many researchers for nearly three decades [1, 3, 16]. This dynamics is governed by underlying nonlinear kinetics and manifests itself as multistability and periodiC., multiperiodic or chaotic oscillations in perfectly stirred systems. At the same time, the investigations of spatial systems have mainly been confined to consideration of classical kinds of waves, or “autowaves” [1, 4]. This term means that a local event, e.g. a pulse generated by a cell, is transferred by diffusion to neighbouring points. Such transport triggers the similar events there, and thus gives rise to a travelling wave. Diffusion plays rather a passive role here and dynamics of the whole medium is determined by dynamic properties of its local elements. Rashevsky  and Turing  found, however, that diffusion may be as important for a system’s dynamics as its local kinetics. That means that behaviour of a spatial system may be far more complex than one can conceive from consideration of its local characteristics. Turing  was the first who clearly described the possible destabilizing role of diffusion.
KeywordsHopf Bifurcation Spatial System Turing Instability Homogeneous Steady State Diffusive Instability
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